Computer Networks · M2 · mocks
Q2 · Pure ALOHA throughput
M2 mock A
Q1(a)+Q1(b) compulsory; choose any two of Q2/Q3/Q4 · 10 marks attempted
Question. A Pure ALOHA channel sends 500-bit frames at 500 kbps. The aggregate attempt rate is 500 frames/s. Find G, normalized throughput and successful frames/s. [3 practice marks]
Answer
Given
| Symbol | Given |
|---|---|
| L | 500 bits |
| R | 500 kbps = 500,000 bits/s |
| λ | 500 aggregate attempts/s |
To find
T, G, S, successful frames/s and bit/s.
Formula and why
LaTeX: T=L/R
LaTeX: G=\lambda T
LaTeX: S=G e^{-2G}
LaTeX: F_{\mathrm{success}}=S/T,\qquad B_{\mathrm{success}}=SRFirst normalize attempts by frame time. Then apply the correct ALOHA model and convert S back to requested rate units.
Step-by-step solution
Step 1. Frame transmission time
T = 500/500,000 = 0.001 s = 1 ms.
Step 2. Offered load
G = 500 × 0.001 = 0.5 attempts/frame time.
Step 3. Exponent and exponential
−2G = -1; e to that power ≈ 0.367879441.
Step 4. Normalized throughput
S = 0.5 × 0.367879441 ≈ 0.183939721.
Step 5. Successful frames each second
S/T = 0.183939721/0.001 ≈ 183.939721 frames/s.
Step 6. Successful frame bit rate
SR = 0.183939721 × 500,000 ≈ 91969.860293 bits/s ≈ 91.969860 kbps.
Final answer: G=0.5, S≈0.183940, successful rate≈183.940 frames/s = 91.970 kbps.